A New Polar Representation for Pell and Pell-Lucas Split Quaternions
Faik Babadag *
Department of Mathematics, Kirikkale University, Kirikkkale, 71450, Turkey.
Ali Atasoy
Keskin Vocational School, Kirikkale University, Kirikkale, 71800, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we define split quaternions with components including Pell and Pell-Lucas number sequences. By using Binet's formulas and Cayley-Dickson's notation we introduce a new polar representation for split quaternions. This alternative representation, based on two complex number sequences, provides a new perspective on the structure of Pell and Pell-Lucas split quaternions and give a deeper understanding of their geometric interpretations and transformations. Furthermore, some fundamental properties and identities for these type of Pell and Pell-Lucas split quaternions are studied. In further the current paper, it would be valuable to replicate similar approaches polar representationin with Pell and Pell-Lucas Split quaternions.
Keywords: Pell split quaternions, pell-Lucas split quaternions polar representation